Frequency Response Function (FRF)
Dr Michael Sek
1
FREQUENCY RESPONSE FUNCTION (FRF)
The concept of Frequency Response Function (Figure 1) is at
the foundation of modern experimental system analysis. A
linear system such as an SDOF or an MDOF, when subjected
to sinusoidal excitation, will respond sinusoidally at the same
frequency and at specific amplitude that is characteristic to the
frequency of excitation. The phase of the response, in general
case, will be different than that of the excitation. The phase
difference between the response and the excitation will vary
with frequency. The system does not need to be excited at one
frequency at the time. The same applies if the system is
subjected to a broadband excitation comprising a blend of
many sinusoids at any given time, such as in the white noise
(Gaussian random excitation) or an impulse. It is obvious that,
in order to find how the system responds at various
frequencies, the excitation and the response signals must be
subjected to the DFT.
The characteristics of a system that describe its response to
excitation as the function of frequency is the Frequency
Response Function H(f) defined as the ratio of the complex
spectrum of the response to the complex spectrum of the
excitation. The spectra are raw (unfolded two-sided).
)(
)(
)(
fF
fX
fH =
The H(f) is a spectrum whose magnitude |H| is the ratio of
|X| / |F| and the phase φ
H
= φ
X
- φ
F
.
Figure 2 shows an example of experimental setup.
Figure 1 Concept of Frequency Response Function
(Brüel&Kjær "Structural Testing")
Figure 2 Car body undergoing testing to acquire its FRFs (Brüel&Kjær "Structural Testing")